Existing Works: Suppose \(r_i=0\) , i.e., we approximate the footprint of the robot through a single circle. In that case, the optimization has a special form that can be solved efficiently through a technique called convex-concave procedure (CCP) [1]}. In comparison, the multi-circle approximation is devoid of such structures due to the presence of orientation variables in (). As a result, one needs to adopt techniques like sequential quadratic programming (SQP) [2]}, [3]} accessed via frameworks like ACADO [4]}. In the context of reactive one-step planning, works like [5]}, [6]} have shown good results for navigating rectangular robots in dynamic environments. However, this setting is slightly orthogonal to our multi-step trajectory optimization set-up that performs planning over long horizons (around 30s).
